To solve the proportion \( \frac{7}{\frac{1}{4}} = \frac{8}{x} \), we can first simplify the left side.
To divide by a fraction, we multiply by its reciprocal. Thus, we have:
\[ \frac{7}{\frac{1}{4}} = 7 \times 4 = 28. \]
Now, the proportion can be rewritten as:
\[ 28 = \frac{8}{x}. \]
Next, we can cross-multiply to solve for \( x \):
\[ 28x = 8. \]
Now, divide both sides by 28 to isolate \( x \):
\[ x = \frac{8}{28}. \]
This fraction can be simplified:
\[ x = \frac{2}{7} \quad \text{(by dividing the numerator and the denominator by 4)}. \]
Therefore, the unknown number \( x \) in the proportion is:
\[ \boxed{\frac{2}{7}}. \]
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